Download A2.A.64: Using Inverse Trigonometric Functions 4

Regents Exam Questions
A2.A.64: Using Inverse Trigonometric Functions 4
Name: ________________________
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A2.A.64: Using Inverse Trigonometric Functions 4: Use inverse functions to find the measure of
an angle, given its sine, cosine, or tangent
Ê
8 The value of cos ÁÁÁ Arc tan
Ë
1 The value of sin(Arc cos1) is
2 The value of tan(Arc sin 1) is
3 If   Arc cos
ˆ
3 ˜˜˜ is
¯
ÁÊ
3 ˜ˆ
9 What is the value of tan ÁÁÁÁ Arc cos  ˜˜˜˜ ?
5¯
Ë
2
, what is the value of tan  ?
2
ÊÁ
5 ˆ˜
10 What is the value of y if y  sin ÁÁÁ Arctan ˜˜˜˜ ?
ÁË
12 ¯
4 If f(x)  sin(Arc tanx), the value of f (1) is
ÊÁ
5 ˆ˜
11 What is the value of tan ÁÁÁ Arc cos ˜˜˜˜ ?
ÁË
13 ¯
ˆ
ÊÁ
ÁÁ
3 ˜˜˜˜
Á
˜ is
5 The value of cos ÁÁ Arc sin
ÁÁ
2 ˜˜˜
¯
Ë
ÊÁ
15 ˆ˜
12 What is the value of tan ÁÁÁ Arc cos ˜˜˜˜ ?
ÁË
17 ¯
ÁÊ
1 ˜ˆ
6 If y  sin ÁÁÁÁ Arc cos ˜˜˜˜ , the value of y is
2¯
Ë
ÊÁ 5 ˆ˜
13 If sin 1 ÁÁÁ ˜˜˜˜  A, then
ÁË 8 ¯
5
1) sinA 
8
8
2) sinA 
5
5
3) cos A 
8
8
4) cos A 
5
ÊÁ
1 ˆ˜
7 What is the exact value of cos ÁÁÁ Arc sin ˜˜˜˜ ?
ÁË
2¯
1
Regents Exam Questions
A2.A.64: Using Inverse Trigonometric Functions 4
Name: ________________________
www.jmap.org
ˆ
ÊÁ
ÁÁ
3
3 ˜˜˜˜
Á
˜˜ 
, then k is
14 If tan ÁÁ Arc cos
ÁÁ
k ˜˜
3
¯
Ë
4
21 If cos x   and tan x  0, the value of sin x is?
5
4
22 If cos    and  lies in Quadrant II, what is the
5
value of tan  ?
ÊÁ
2 ˆ˜
15 What is a value of cos ÁÁÁÁ Arc tan ˜˜˜˜ ?
3¯
Ë
16 If cos   
7
and A terminates in Quadrant IV,
25
tanA equals
23 If sinA  
5
and sin   0, then tan  is
13
2
and angle x lies in the second
3
quadrant, what is the value of cos x?
17 If tanx  
18 If x is a positive acute angle and cos x 
4
and A is in Quadrant I, what is the
5
value of sinA  tan A?
24 If cos A 
3
, what
4
3
25 If sin    and cos   0, what is the value of
5
tan  ?
is the exact value of sin x?
26 If  is a positive acute angle and sin   a, which
expression represents cos  in terms of a?
3
19 If cos    and tan  is negative, the value of
4
sin  is
20 If sin  
ÊÁ
1 ˆ˜
27 What is the value of sin ÁÁÁ Arc cos ˜˜˜˜ ?
ÁË
x¯
7
3
and cos    , what is tan  ?
4
4
2
ID: A
A2.A.64: Using Inverse Trigonometric Functions 4: Use inverse functions to find the measure of
an angle, given its sine, cosine, or tangent
Answer Section
1 ANS:
0
REF: 019921siii
2 ANS:
undefined
REF: 010221siii
3 ANS:
1
REF: 068427siii
4 ANS:
2
2
REF: 060023siii
5 ANS:
1
2
REF: 069916siii
6 ANS:
3
2
REF: 088618siii
7 ANS:
3
2
REF: 061008b
8 ANS:
1
2
REF: 089320siii
9 ANS:
4

3
REF: 080123siii
1
ID: A
10 ANS:
5
13
REF: 089817siii
11 ANS:
12
5
REF: 060322siii
12 ANS:
8
15
8
17
8
15
8

If sin   , then cos   . tan  
15 15
17
17
17
REF: 081508a2
13 ANS: 1
14 ANS:
2
tan 30 
REF: 011112a2
3
3
 30
. Arc cos
3
k
3
k
 cos 30
k 2
REF: 061323a2
15 ANS:
3 13
13
REF: 060225siii
16 ANS:
12

5
REF: 068417siii
17 ANS:

3 13
13
REF: 068632siii
2
ID: A
18 ANS:
13
4
REF: 080604b
19 ANS:
7
4
REF: 019431siii
20 ANS:

7
3
REF: 010321siii
21 ANS:
3

5
REF: 018628siii
22 ANS:
3

4
3
5
sin 
3
4
3


If cos    and  lies in Quadrant II, then sin   . tan  
4
4
cos 
5
5

5
REF: 061004b
23 ANS:
7

24
7
25
sinA
7
7
24


If sin A   , cos A  , and tanA 
25
25
cos A
24
24
25

REF: 011413a2
24 ANS:
9
20
REF: 069421siii
3
ID: A
25 ANS:
3

4
REF: 010021siii
26 ANS:
1  a2
REF: 060418b
27 ANS:
x2  1
x
REF: 010029siii
4